Purpose :
Experiments recording tear film thickness reveal localized tear break up (TBU); however, there seems to be multiple causes of local TBU. Our goal is to better understand the causes of TBU by studying a mathematical model for tear film dynamics. To our knowledge, this is the first study of TBU using a mobile lipid layer with variable resistance to evaporation. We aim to reveal details of TBU from physically reasonable parameters and conditions caused by elevated evaporation due to lipid defects, and how this process can be aided by surfactant-driven Marangoni flow.

Methods :
We study a math model for TBU including a mobile aqueous layer; a mobile lipid layer; tear viscosity; evaporation depending on lipid thickness and environmental humidity; osmosis from the epithelium; surface tension at the layer surfaces; and surface tension variation at the aqueous-lipid interface caused by polar lipid surfactants (Marangoni effect). We simulate this system for a variety of reasonable parameter values and analyze the results. We which effects contribute to localized TBU in some cases, then compare with in vivo experiments of King-Smith et al. (2013, IOVS 54:4900).

Results :
Case A involves a lipid defect, such as a hole in the lipid layer with reduced resistance to evaporation. Results show the lipid defect causes elevated evaporation, resulting in local thinning. Evaporatively-driven thinning competes with surface-tension-driven aqueous flow toward the TBU region, however evaporation is dominant. This thinning can cause TBU and elevated osmolarity over several seconds, which is consistent with TBU seen in experiment. Case B considers simulations containing a region of significantly elevated surfactant concentration in the lipid layer. The surfactant drives flow in both layers, and rapidly creates a local thin region in the lipid layer (in well under a second) that changes little thereafter. The thin lipid results in increased thinning, and subsequent evaporative TBU over several seconds. Case B is remarkably similar to the results of Figure 6 in King-Smith et al (2013).

Conclusions :
A mathematical model for tear film TBU with a dynamic lipid layer was studied. Evaporation through a thin local defect can lead to TBU in the model. The model can also capture Marangoni driven effects that cause local defects in the lipid layer leading to local TBU as seen experimentally.

This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.